Proportional integrator squared (pi) 2 speed controller for utilization in a speed regulator system

ABSTRACT

A speed controller for utilization in a speed regulator system for a d.c. motor. An operational amplifier receives a voltage V1 through a first resistor R1, the voltage V1 being a function of the instantaneous speed of the d.c. motor. A second input to the operational amplifier is a speed reference signal. A feedback path connects the first input resistor R1 with an adjustable portion Alpha of the amplifier output Vo. The feedback path includes a second resistor R2 serially with capacitors C1 and C2; a third resistor R3 is connected between the union of capacitors C1 and C2 and ground. The speed controller is a proportional integrator squared (PI)2 having the Laplace transfer function:

United States Patent 1 Peterson et al.

[111 3,775,653 Nov. 27, 1973 [75] Inventors: Robert S. Peterson; MelvinA.

Hensleigh, both of Williamsville, N.Y. 14221 [73] Assigneez WestinghouseElectric Corporation;

Pittsburgh, Pa.

22 Filed: Jan.16,1973 21 App1.No.:324,054

[52] US. Cl 318/326, 318/332, 318/331 [51] Int. Cl. 1102p 5/16 [58]Field of Search 318/326, 327, 332,

[56] References Cited UNITED STATES PATENTS 12/1971 OCallaghan ..3l8/3269/1972 Nakajima 318/327 SIGNAL Primary Examiner-Bernard A. GilheanyAssistant Examiner-Thomas Langer Att0rneyF. Shapoe et a1.

[ 5 7] ABSTRACT A speed controller for utilization in a speed regulatorsystem for a d.c. motor. An operational amplifier receives a voltage Vthrough a first resistor R the voltage V being a function of theinstantaneous speed of the do motor. A second input to the operationalamplifier is a speed reference signaL, A feedback path connects thefirst input resistor R, with an adjustable portion a of the amplifieroutput V0. The feedback path includes a second resistor R serially withcapacitors C, and C a third resistor R is connected between the union ofcapacitors C and C and ground. The speed controller is a proportionalintegrator squared (Pl) having the Laplace transfer function:

PATENTEDNBV271975 v N 3775.653

' sum 2 OF 3 I 1 v Wv (VOLT-S) (VOLTS) SPEED {R4 REFERENCE FIG. 2.SIGNAL 7 (PI) SPEED CONTROLLER C (PI) SPEED CONTROLLER FREQUENCY 0L)FIG.4A

PATENTEDNOvz? 191s 3.775.653

SHEET 3 [IF 3 STAN D SPEED ERROR O\fi "-05 SEC- TIME DRIVE ARM. CURRTIME IMPACT LOAD RESPONSE OF PI SPEED CONTROLLER STAND SPEED ERROR A c oM s .05 SEC. (H TIME DRIVE 7 TlME- IMPACT LOAD RESPONSE OF P1 SPEEDCONTROLLER .PROPORTIONALINTEGRATOR SQUARED (PI) 2 SPEED CONTROLLERFORUTILIZATION IN A SPEED REGULATOR SYSTEM BACKGROUND OF THEINVENTION 1. Field of the Invention This invention relates to a speedregulator system for a d.c. motor, and more'specitically to a speedcontroller for utilization with such a system.

'2. Description of the Prior Art:

In bar, roll and stretch mills when the material being processed leavesone roller stand and proceeds to the next stand, there is aresultingspeed drop due to the impact of the material upon entry into thesucceeding stand. In somesituations the loss'in speed is of sufficientmagnitude to develop a loop sufficiently large so as to rub on theadjacent structure thereby damaging the material.

in tension, itis customary to anticipate the change by displacing themill screws ahead of the interstand tension zone. The change in screwdisplacement is always such as toworsen the gauge error. This is broughtabout by the necessary trade off between roll force and tension.

As an example, considerthe case where the processed material has beenreduced in gauge and thick I (unprocessed) material iswelded to thethinnerIprocessed) material. As the welded joint goes'through the standthere is a lower load on the mill motor, and it responds by speeding up,thus buildingtension. in the material. In order to bring the materialback to apreset magnitude, it is necessary to displace the screws in adownward direction in the process of trading off roll force for tension.As the screws come down, the roll gauge is narrowed, thus making thegauge smaller, possibly allowing off-gauge material to pass through; Ifno adjustment is made in the screws, the gauge in the vicinity of theweld will be better, but there is always the possibility of having toolittle tension or too much tension. It is therefore necessary toestablish some maximum and minimum tension standards. If the tension istoo low, the roll force may become high enough to cause a pinch in thematerial. (A pinchis a momentary pause in the moving strip which cancause serious 7 SUMMARY OF THE INVENTION This invention relates to aspeed regulator system for a d.c. motor having a unique speed controllermeans.

An operational amplifier means has a first input, a second input and anoutput with a feedback path connected between the first input and anadjustable portion of the output. The first input receives a signalwhich is a function of the" instantaneous speed of the motor while thesecond inputreceives a speed reference signal. First and secondresistance means and first and second capacitance means are in saidfeedback path, the first resistance means and said first and secondcapacitance means being serially connected, the second resistance meansbeing connected between the union of the first and second capacitancemeans and ground. The speedcontroller means acts as a proportionalintegrator squared.

; BRIEF DESCRIPTION or TI-IEDRAWINGS FIG. 1 is a block diagramdisclosing a speed regulator system for a d.c. motor, the speedcontroller of the invention being a component part of the speedregulator system; I

FIG. 2 is an electrical schematic of the proportional integrator squared(PI) speed controller of the instant invention;

FIGJS is an open loop Bode plot for comparing the (PI) speed controllerof the invention, with the PI speed controller of the .prior art;

FIG. 4A depicts the impact load response of the prior art PI speedcontroller, and 7 FIG. 4B depicts the impact load response of the (PI)speed controller of the instant invention.

DESCRIPTION OF AN EXEMPLARY EMBODIMENT Referringnow to FIG. 1 there isshown a speed regulator systemfor one or more d.c. mill motors. Forsimplicity, a single drive, single converter speed regulator system. isdepicted, although it will be appreciated that the invention is equallyapplicable with dual converters as well as duplex or multi-motor drives.

A single converter drive is one in which thereare no regenerativecapabilities available in the thyristor source for the thyristor isindicated at 14. The thyristor converter 12 converts the a.c. power tocontrollable d.c. power. The regulator system incorporates two cascadedminor loops namely: the voltage and current loops. The minorvoltage-loopcomprises a voltage controller 16, a gate pulse generatorand amplifier 18, a voltage sensor 20 and a reverse current simulator22. The current loop comprises a current-controller 24, the minorvoltage loop, and a current sensor 26. A set of threecurrenttransformersindicated'syrnbolically at 28 supply a-feedbackvoltage signal-(ia) to the current sensor 26 whichdelivers'a signal i,,to thecurrent controller 24. The current loop controls the motor currentby controlling the bus voltage signal 'Vb* to the voltage controller 16.The voltage loop controls the thyristor converter l2-outputbusvoltage+Vb as a function of the voltage signal -Vb* andthe feedbackvoltage signal+Vb supplied by the voltage sensor 20. The voltagecontroller 16 controls the gating angle of the thyristor The main'speedregulator loop includes a speed controller 30 and a tachometer generator32 connected to the shaft of the d.c. motor 10. This loop regulates themotor speed, by comparing in the speed controller-30, the referencevoltageto a voltage V, from the tachometer generator 32 which isproportional to motor speed. The output of the speed controller 30provides the reference l,,* to the current controller 24.

Completing the description of FIG. 1, the reverse current simulator 22prevents the current controller 24 from going into reverse saturationshould .the speed controller 30 so demand on slowdown, sincethe drivesystem is not capable of regeneration or reverse current.

Finally, if for some reason the armature currentexceeds the currentlimit value, a systems fault is indicated. When this happens, a pulsesignal is released from thecurrent sensor 26 which instantaneouslysuppresses all further pulsing in the gate pulse generator 18. Thus, thefault currentis confined to the last conducting thyristors in' thethyristor converter 12.

The speed controller of the invention is shown in FIG. 2, and comprisesan operational amplifier indicated generally at 34 having inputresistors R and R amplifier 36 and output potentiometer 38, having anadjustable gain a, the slide of the potentiometer 38 being connected ina feedback path indicated generally at 40 to the input of amplifier 36.The feedback path 40 includes serially connected resistor R andcapacitors C, and C resistor R connected between the union ofcapacitorsC and C and ground.

v The Laplace transfer function of the speed controller is:

2 1 s(C1+C2)Sl-1 V1 0 3 8 CzRaS (1) When the transfer function is brokendown there obtains: I i

The prior art has provided a speed controller having proportionalintegration (PI) properties. In the Laplace transfer function ofequations (2) and (3), within each the first term in the bracketprovides'the proportional part, and the second term within each bracketprovides the integrating part as indicatedfby the 1/8 operator. Thespeed controller is'therefore identified as a (PI) operationalamplifier..

Open loop Bode plots of the respective speed loops for PI and (PI) speedcontrollers are depicted in FIG.

3. As maybe observed for a study of these plots, the

crossover frequency w is the same for both PI and (PI) speedcontrollers. Thus the transient stability for bothcontrollers issubstantially the same.

Performance" characteristics for the (PI) and (PI) controllers areempirically demonstrated in FIGS. 4A and 4B. In FIG. 4A there is shownthe input and .4 response of a PI speed controller. The stand speederror A1 is finite and substantial. In FIG. 48 there is shown the impactload response of a (PI)- speed controller. The error is substantiallyzero sincethe areas A =areaB+area C.

Using the final value theorem, it can be demonstrated that the i (whichis the speed error with respect to time) is 0.002 per unit seconds forthe prior art speed controller (PI) and 0 per unit seconds (no stripstorage) for the (PI) speed controller.

What we claim is: 1. In a speed regulator system for a d.c. motor, aspeed controller means comprising:

a. operational amplifier means controlling said motor and having a firstinput, a second input, an output, and a feedback path'connected betweensaid first input and an adjustable portion of said output; said 7 firstinput receiving a signal which is a function of the instantaneous speedof said motor, said second input receiving a speed reference signal;

b. first and second resistance means in said feedback path;

c. first and second capacitance means in said feedback path, said firstresistance means and said first and second capacitance means beingserially connected, said second resistance means being connected betweenthe union of the first and second capacitance means and ground, saidspeed controller having the characteristics of a proportional integratorsquared.

2. Speed controller means according to claim 1 wherein said secondcapacitance means is very much greater than said first capacitancemeans.

3. Speed controller means according to claim 1 wherein said outputincludes a potentiometer having a sliding member, the position of saidsliding member defining said adjustable portion.

4. In a speed regulator system for a d.c. motor, a speed controllermeans comprising:

a. operational amplifier means controlling said motor and having a firstinput resistor (R a second input, an output having an output voltage(V,) and a feedback path connected between said first input resistor andand adjustable portion (a) of said output, said first input resistorreceiving an input signal (Vo) which is a function of the instantaneousspeed of said d.c. motor, said second input receiving a speedreference'signal;

b. second and third resistors (R 3 insaid feedback path;

c. first and second capacitors in said feedback path,

said second resistor R and said first and second capacitors (C C beingserially connected, said third resistor (R being connected between theunion of the first and second capacitors and ground, whereby the speedcontroller has the Laplace transform:

w wa

than the first capacitor C

1. In a speed regulator system for a d.c. motor, a speed controllermeans comprising: a. operational amplifier means controlling said motorand having a first input, a second input, an output, and a feedback pathconnected between said first input and an adjustable portion of saidoutput; said first input receiving a signal which is a function of theinstantaneous speed of said motor, said second input receiving a speedreference signal; b. first and second resistance means in said feedbackpath; c. first and second capacitance means in said feedback path, saidfirst resistance means and said first anD second capacitance means beingserially connected, said second resistance means being connected betweenthe union of the first and second capacitance means and ground, saidspeed controller having the characteristics of a proportional integratorsquared.
 2. Speed controller means according to claim 1 wherein saidsecond capacitance means is very much greater than said firstcapacitance means.
 3. Speed controller means according to claim 1wherein said output includes a potentiometer having a sliding member,the position of said sliding member defining said adjustable portion. 4.In a speed regulator system for a d.c. motor, a speed controller meanscomprising: a. operational amplifier means controlling said motor andhaving a first input resistor (R1), a second input, an output having anoutput voltage (V1) and a feedback path connected between said firstinput resistor and and adjustable portion ( Alpha ) of said output, saidfirst input resistor receiving an input signal (Vo) which is a functionof the instantaneous speed of said d.c. motor, said second inputreceiving a speed reference signal; b. second and third resistors(R2,R3) in said feedback path; c. first and second capacitors in saidfeedback path, said second resistor R2 and said first and secondcapacitors (C1,C2) being serially connected, said third resistor (R3)being connected between the union of the first and second capacitors andground, whereby the speed controller has the Laplace transform:
 5. Aspeed controller means according to claim 4 wherein the second capacitorC2 is very much greater than the first capacitor C1.